Using Markov Chain and Nearest Neighbor Criteria in an Experience Based Study Planning System with Linear Time Search and Scalability

Abstract

Most automated rule-based expert systems developed to aid student study planning and advising have appeared to be ephemeral due to the dynamic property in the ever-changing curricular requirements and rules. We propose a novel case-based study planning system with the search criteria based on the experience-indicated probability in Markov chains and the nearest-neighbor measurement for matches. We provide query results of course sequences to students who need to meet certain constraints such as to graduate within a certain number of academic terms, maintaining a minimal grade-point average, etc., all drawn from past graduate records. The time complexity of computing the nearest-neighbor indices to find the maximum similarity can be very large. Our implementation method achieves a linear-time complexity in both searching and scaling the system. When updating with a new record, each parametric combination represented by a sorted list of the records is linearly looked up, and the new record value is inserted to keep the list sorted. Since each query input is a set of constraints in a pre-determined order, the parametric combinations have an associated sorted list to look up in a one-pass linear process. The first-order Markov chains can also be updated with a linear time complexity whenever a new graduate record is introduced. The probability matrix is first looked up by row and then column, representing a pair of courses taken in two adjacent academic terms, and the look-up time is also linear